Download visible Ultra violet Infra red Longer line ? Energy? Wavelength

hc
ΔE = hν =
λ
Infra red visible Longer line ? Energy? Wavelength ? Emission spectra Ultra violet Frequency? hc
ΔE = hν =
λ
Infra red visible absorp2on Ultra violet emission, absorpAon, ionizaAon n = ∞ E n =4 n=3 n=2 n=1 Closer to nucleus? de Broglie wavelength Einstein discovered that
a photon has momentum p given by
E photon hν
p=
=
c
c
and since
c
h
h
ν = we have p = or λ =
λ
λ
p
h
h
Perhaps ? λ = =
for a material particle
p mv
Light beams interfere with each other Difffrac2on is characteris2c of wave mo2on In phase reinforce Out of phase cancel Dual nature of ma@er (par2cle and/or wave ) was confirmed by Davisson and Germer and independently by G. P. Thomson both in 1927 X-­‐rays going through Al foil Electrons going through Al foil This duality is the basis for the electron microscope 6 How can an electron be both a par2cle and a wave? Our vocabulary , built on our observa2ons of the (macroscopic) world around us, is unable to characterize its nature more precisely. It behaves according to the laws of Quantum Mechanics 8 What about other par2cles? Do they also have dual character? Yes, but! For the wave character of a “par2cle” to be observable its wave length has to be comparable to the distances between atoms in a material 9 What is the deBroglie wavelength of a 15 gram golf ball moving at 160 km/hour? h
6.626 × 10 −34 Js
λ= =
≈ 10 −33 m
p 15g × 1kg × 160 km × 10 3 m × 1h
1000g
h
km 3600s
Too small to be no2ced Compare to an electron moving at 0.1 the speed of light h
6.626 × 10 −34 Js
−11
λ= =
≈
2.4
×
10
m
−31
8
−1
p 9.1× 10 kg × 0.3 × 10 ms
Comparable to the spacing between atom in materials 10 Only electrons and very light atoms have deBroglie wavelengths that are large enough to affect their proper2es. 11 Heisenberg Uncertainty Principle Lecture notes 16 Puts constraints on what we can know about a system We cannot see individual molecules using visible radia2on Wavelength of visible light is much larger than the molecule Reduce wavelength and increase resolu2on Frequency increases Energy of radia2on increases Momentum of photon increases 12 Heisenberg Uncertainty Principle Suppose we wanted to observe an electron We need a small wavelength (high energy) photon electron photon 13 Heisenberg Uncertainty Principle Suppose we wanted to observe an electron We need a small wavelength (high energy) photon electron photon 14 Heisenberg Uncertainty Principle electron ΔxΔpx ≥ h
photon By the 2me you see the photon the electron has moved 15 Heisenberg Uncertainty Principle Puts constraints on what we can know about a system We cannot know both the loca2on and momentum of a par2cle with arbitrary precision Bohr model cannot be correct! 16 Lecture notes 16 Schrodinger (1926) Inspired by deBroglie’s ideas he derived an equa2on that described the electron in the H atom as a standing wave When he solved this equa2on he obtained the allowed energy levels of the hydrogen atom 17 Energy levels found by Schrodinger where iden2cal to those found by Bohr! RJ
En = − 2
n
Instead of orbits the electron moves in regions of space called orbitals In the Bohr model the orbit was characterized by one quantum number n which could be any posi2ve integer. 18 In the Schrodinger theory there are 3 quantum numbers Symbol name values allowed significance n principal 1,2,3,… energy l secondary 0, 1, 2, n-­‐1 shape m magne2c –l to +l orienta2on integer increments Secondary quantum number (determines angular momentum of electron) is oLen designated by a leMer l 0 1 2 3 4 le@er s p d f g 19 The energy in the H atom depends only on the n quantum number RJ
En = − 2
n
20 Note the rela2onship between the quantum numbers n=1; l=0 ; m=0 ; 1s 1 orbital n=2 ; l=0 ; m=0 ; 2s l=1 ; m=-­‐1,0,+1 ; 2p 4 orbitals n=3 ; l=0 ; m=0 ; 3s 9 orbitals l=1 ; m=-­‐1,0,+1 ; 3p l=2; m=-­‐2,-­‐1,0,+1,+2 ; 3d n=4 ; l=0; m=0 ; 4s l=1; m=-­‐1,0,+1 ; 4p 16 orbitals l=2 ; m=-­‐2,-­‐1,0,+1,+2 ; 4d l=3; m=-­‐3,-­‐2,-­‐1,0,+1,+2,+3 ; 4f 21 Note the rela2onship between the quantum numbers n=1; 1 orbital n=2 Orbitals with same n consAtute a shell 4 orbitals n=3 9 orbitals n=4 16 orbitals Number of orbitals within a shell is called the degeneracy of the shell The energy in the H atom depends only on the n quantum number 22